AnR-moduleMis called principally quasi-injective if eachR-hornomorphism from a principal submodule ofMtoMcan be extended to an endomorphism ofM. Many properties of principally injective rings and quasi-injective modules are extended to these modules. As one application, we show that, for a finite-dimensional quasi-injective moduleMin which every maximal uniform submodule is fully invariant, there is a bijection between the set of indecomposable summands ofMand the maximal left ideals of the endomorphism ring ofM